Analysis of substrate thermal gradient effects on optimal buffer insertion

This paper studies the effects of the substrate thermal gradients on the buffer insertion techniques. Using a non-uniform temperature-dependent distributed RC interconnect delay model, the buffer insertion problem is analyzed and design guidelines are provided to ensure the near-optimality of the signal performance in the presence of the thermal gradients. In addition, the effect of temperature-dependent driver resistance on the buffer insertion is studied. Experimental results show that neglecting thermal gradients in the substrate and the interconnect lines can result in non-optimal solutions when using standard buffer insertion techniques and that these effects intensify, with technology scaling.